1: static const char help[] ="Minimum surface problem in 2D.\n\
  2: Uses 2-dimensional distributed arrays.\n\
  3: \n\
  4:   Solves the linear systems via multilevel methods \n\
  5: \n\n";

  7: /*

  9:     This example models the partial differential equation

 11:          - Div((1 + ||GRAD T||^2)^(1/2) (GRAD T)) = 0.

 13:     in the unit square, which is uniformly discretized in each of x and
 14:     y in this simple encoding.  The degrees of freedom are vertex centered

 16:     A finite difference approximation with the usual 5-point stencil
 17:     is used to discretize the boundary value problem to obtain a
 18:     nonlinear system of equations.

 20: */

 22: #include <petscsnes.h>
 23: #include <petscdm.h>
 24: #include <petscdmda.h>

 26: extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,void*);

 28: int main(int argc,char **argv)
 29: {
 30:   SNES           snes;
 31:   PetscInt       its,lits;
 32:   PetscReal      litspit;
 33:   DM             da;

 35:   PetscInitialize(&argc,&argv,NULL,help);
 36:   /*
 37:       Set the DMDA (grid structure) for the grids.
 38:   */
 39:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,5,5,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
 40:   DMSetFromOptions(da);
 41:   DMSetUp(da);
 42:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,NULL);
 43:   SNESCreate(PETSC_COMM_WORLD,&snes);
 44:   SNESSetDM(snes,da);
 45:   DMDestroy(&da);

 47:   SNESSetFromOptions(snes);

 49:   SNESSolve(snes,0,0);
 50:   SNESGetIterationNumber(snes,&its);
 51:   SNESGetLinearSolveIterations(snes,&lits);
 52:   litspit = ((PetscReal)lits)/((PetscReal)its);
 53:   PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its);
 54:   PetscPrintf(PETSC_COMM_WORLD,"Number of Linear iterations = %D\n",lits);
 55:   PetscPrintf(PETSC_COMM_WORLD,"Average Linear its / SNES = %e\n",(double)litspit);

 57:   SNESDestroy(&snes);
 58:   PetscFinalize();
 59:   return 0;
 60: }

 62: PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **t,PetscScalar **f,void *ptr)
 63: {
 64:   PetscInt    i,j;
 65:   PetscScalar hx,hy;
 66:   PetscScalar gradup,graddown,gradleft,gradright,gradx,grady;
 67:   PetscScalar coeffup,coeffdown,coeffleft,coeffright;

 70:   hx = 1.0/(PetscReal)(info->mx-1);  hy    = 1.0/(PetscReal)(info->my-1);

 72:   /* Evaluate function */
 73:   for (j=info->ys; j<info->ys+info->ym; j++) {
 74:     for (i=info->xs; i<info->xs+info->xm; i++) {

 76:       if (i == 0 || i == info->mx-1 || j == 0 || j == info->my-1) {
 77:         f[j][i] = t[j][i] - (1.0 - (2.0*hx*(PetscReal)i - 1.0)*(2.0*hx*(PetscReal)i - 1.0));
 78:       } else {

 80:         gradup    = (t[j+1][i] - t[j][i])/hy;
 81:         graddown  = (t[j][i] - t[j-1][i])/hy;
 82:         gradright = (t[j][i+1] - t[j][i])/hx;
 83:         gradleft  = (t[j][i] - t[j][i-1])/hx;

 85:         gradx = .5*(t[j][i+1] - t[j][i-1])/hx;
 86:         grady = .5*(t[j+1][i] - t[j-1][i])/hy;

 88:         coeffup   = 1.0/PetscSqrtScalar(1.0 + gradup*gradup + gradx*gradx);
 89:         coeffdown = 1.0/PetscSqrtScalar(1.0 + graddown*graddown + gradx*gradx);

 91:         coeffleft  = 1.0/PetscSqrtScalar(1.0 + gradleft*gradleft + grady*grady);
 92:         coeffright = 1.0/PetscSqrtScalar(1.0 + gradright*gradright + grady*grady);

 94:         f[j][i] = (coeffup*gradup - coeffdown*graddown)*hx + (coeffright*gradright - coeffleft*gradleft)*hy;
 95:       }

 97:     }
 98:   }
 99:   return 0;
100: }

102: /*TEST

104:    test:
105:       args: -pc_type mg -da_refine 1 -ksp_type fgmres

107:    test:
108:       suffix: 2
109:       nsize: 2
110:       args: -pc_type mg -da_refine 1 -ksp_type fgmres

112:    test:
113:       suffix: 3
114:       nsize: 2
115:       args: -pc_type mg -da_refine 1 -ksp_type fgmres -snes_type newtontrdc -snes_trdc_use_cauchy false

117:    test:
118:       suffix: 4
119:       nsize: 2
120:       args: -pc_type mg -da_refine 1 -ksp_type fgmres -snes_type newtontrdc
121:       filter: sed -e "s/SNES iterations = 1[1-3]/SNES iterations = 13/g" |sed -e "s/Linear iterations = 2[8-9]/Linear iterations = 29/g" |sed -e "s/Linear iterations = 3[0-1]/Linear iterations = 29/g"

123: TEST*/